Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors

Acceptor-bound holes in oxides often localize asymmetrically at one out of several equivalent oxygen ligands. Whereas Hartree-Fock (HF) theory overly favors such symmetry-broken polaronic hole localization in oxides, standard local-density (LD) calculations suffer from spurious delocalization among several oxygen sites. These opposite biases originate from the opposite curvatures of the energy as a function of the fractional occupation number n, i.e., d(2)E/dn(2)< 0 in HF and d(2)E/dn(2)>0 in LD. We recover the correct linear behavior, d(2)E/dn(2)=0, that removes the (de)localization bias by formulating a generalized Koopmans condition. The correct description of oxygen hole localization reveals that the cation-site nominal single acceptors in ZnO, In2O3, and SnO2 can bind multiple holes.